Question: Expand and combine like terms. $(3-8w^2)^2=$
Answer: We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ Since we have a minus sign, let's rewrite the binomial as a sum where the second term is negative, then use the pattern. $\begin{aligned} &\phantom{=}\left(3-8w^2\right)^2 \\\\ &=\left(3+\left(-8w^2\right)\right)^2 \\\\ &=(3)^2+2(3)(-8w^2)+(-8w^2)^2 \\\\ &=9-48w^2+64w^4 \\\\ &=64w^4-48w^2+9 \end{aligned}$